Re: A Property of Boundary of a Set in a Topological Space

Originally Posted by raed

Thank you for your reply actually using that the boundary is closed I proved one inclusion it is not clear for me how to get the converse.
Actually I proved that Bd[Bd{Bd(A)}] is a subset of Bd[Bd(A)] but I could not prove the converse.

Well I have not have any idea what to tell you.
It is clear on that webpage I gave you.
It says "For any set S, ∂S ⊇ ∂∂S, with equality holding if and only if the boundary of S has no interior points, which will be the case for example if S is either closed or open. Since the boundary of a set is closed, ∂∂S = ∂∂∂S for any set S.